The present invention relates to a cigarette having a modified burn rate and a cigarette making apparatus for manufacturing such a cigarette. The modifications to the cigarette of the present invention include changes to the wrapper of the cigarette paper such that the tobacco column of the cigarette is adjacent to a strip wrap forming co-axial zones of high diffusion areas and co-axial zones of low diffusion areas. Such a partial double wrap cigarette exhibits a modified burn rate such that the standard smolder rate of the cigarette may be changed as desired to either self extinguish or slowed significantly depending upon the desired outcome.